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Putnam 2004 B4

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December 11, 2004
Putnamrotationanalytic geometrygeometrygeometric transformationcollege contestsPutnam complex

Problem Statement

Let nn be a positive integer, n≥2n \ge 2, and put θ=2πn\theta=\frac{2\pi}{n}. Define points Pk=(k,0)P_k=(k,0) in the xy-plane, for k=1,2,…,nk=1,2,\dots,n. Let RkR_k be the map that rotates the plane counterclockwise by the angle θ\theta about the point PkP_k. Let RR denote the map obtained by applying in order, R1R_1, then R2R_2, ..., then RnR_n. For an arbitrary point (x,y)(x,y), find and simplify the coordinates of R(x,y)R(x,y).
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